We present the syntax and proof theory of a logic of argumentation, LA. We also outline the development of a category theoretic semantics for LA. LA is the core of a proof theoretic model for reasoning under uncertainty. In this logic, propositions are labeled with a representation of the arguments which support their validity. Arguments may then be aggregated to collect more information about the potential validity of the propositions of interest. We make the notion of aggregation primitive to the logic, and then define strength mappings from sets of arguments to one of a number of possible dictionaries. This provides a uniform framework which incorporates a number of numerical and symbolic techniques for assigning subjective confidences to propositions on the basis of their supporting arguments. These aggregation techniques are also described with examples.

The application of an interactive theorem-proving assistant and specification support tool called mural in the specification and verification of a small Vienna development method (VDM) development is described. It is the authors' intention to give a feel for how mural works and of mural's applicability as a tool in specifying and verifying software.>